Elastic Wave Equation

Geophysics · 1828

Equation: ρ·∂²u/∂t² = (λ+μ)∇(∇·u) + μ∇²u
Field: Geophysics
Named After: Claude-Louis Navier · Augustin-Louis Cauchy · Siméon Poisson
Year: 1828

Symbols

u displacement of the rock · ρ density · λ, μ the Lamé constants (compressibility and rigidity) · t time · the two terms carry two different wave types

Significance

Newton's second law written for solid rock — and Poisson noticed the equation splits into two independent waves: compressional and shear. Every seismogram is this equation's solution, rung through the body of the Earth.